If you have a scale & 50 coins all at the same weight with the exception of 1, either lighter or heavier, which you will not know, what is the least amount of times you would need to use the scale?

Answer 1

You would need to use the scale 2 times to determine which coin is either lighter or heavier.

First, divide the 50 coins into two groups of 25 each and weigh them. If the scale balances, then the different coin is in the remaining 25 coins. If the scale does not balance, then the different coin is in one of the two groups of 25.

Second, take the group of 25 coins that contains the different coin and divide them into two groups of 12 and 13 coins. Weigh these two groups. If the scale balances, then the different coin is one of the remaining 12 coins. If the scale does not balance, then the different coin is in one of the two groups of 12.

By following this method, you can determine which coin is either lighter or heavier in just 2 uses of the scale.